# Properties

 Label 2960.2 Level 2960 Weight 2 Dimension 134288 Nonzero newspaces 78 Sturm bound 1050624 Trace bound 32

## Defining parameters

 Level: $$N$$ = $$2960 = 2^{4} \cdot 5 \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$78$$ Sturm bound: $$1050624$$ Trace bound: $$32$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2960))$$.

Total New Old
Modular forms 266688 136180 130508
Cusp forms 258625 134288 124337
Eisenstein series 8063 1892 6171

## Trace form

 $$134288 q - 136 q^{2} - 104 q^{3} - 128 q^{4} - 254 q^{5} - 384 q^{6} - 96 q^{7} - 112 q^{8} - 28 q^{9} + O(q^{10})$$ $$134288 q - 136 q^{2} - 104 q^{3} - 128 q^{4} - 254 q^{5} - 384 q^{6} - 96 q^{7} - 112 q^{8} - 28 q^{9} - 200 q^{10} - 292 q^{11} - 144 q^{12} - 160 q^{13} - 144 q^{14} - 118 q^{15} - 432 q^{16} - 288 q^{17} - 120 q^{18} - 52 q^{19} - 192 q^{20} - 452 q^{21} - 128 q^{22} - 72 q^{23} - 128 q^{24} - 34 q^{25} - 384 q^{26} - 116 q^{27} - 160 q^{28} - 140 q^{29} - 272 q^{30} - 380 q^{31} - 176 q^{32} - 356 q^{33} - 240 q^{34} - 182 q^{35} - 544 q^{36} - 198 q^{37} - 432 q^{38} - 148 q^{39} - 376 q^{40} - 164 q^{41} - 288 q^{42} - 88 q^{43} - 256 q^{44} - 306 q^{45} - 480 q^{46} - 32 q^{47} - 224 q^{48} - 292 q^{49} - 312 q^{50} - 252 q^{51} - 208 q^{52} - 168 q^{53} - 224 q^{54} - 122 q^{55} - 432 q^{56} + 44 q^{57} - 176 q^{58} - 52 q^{59} - 136 q^{60} - 540 q^{61} - 64 q^{62} - 160 q^{63} - 80 q^{64} - 386 q^{65} - 256 q^{66} - 208 q^{67} - 16 q^{68} - 204 q^{69} - 40 q^{70} - 412 q^{71} + 128 q^{72} + 44 q^{73} - 48 q^{74} - 536 q^{75} - 224 q^{76} - 164 q^{77} + 128 q^{78} - 284 q^{79} - 24 q^{80} - 856 q^{81} - 280 q^{83} + 144 q^{84} - 250 q^{85} - 272 q^{86} - 340 q^{87} + 80 q^{88} + 12 q^{89} + 32 q^{90} - 348 q^{91} - 144 q^{92} - 68 q^{93} - 80 q^{94} - 266 q^{95} - 336 q^{96} - 248 q^{97} - 216 q^{98} - 252 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2960))$$

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space $$S_k^{\mathrm{new}}(N, \chi)$$ we list available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
2960.2.a $$\chi_{2960}(1, \cdot)$$ 2960.2.a.a 1 1
2960.2.a.b 1
2960.2.a.c 1
2960.2.a.d 1
2960.2.a.e 1
2960.2.a.f 1
2960.2.a.g 1
2960.2.a.h 1
2960.2.a.i 1
2960.2.a.j 1
2960.2.a.k 1
2960.2.a.l 1
2960.2.a.m 1
2960.2.a.n 1
2960.2.a.o 2
2960.2.a.p 2
2960.2.a.q 2
2960.2.a.r 3
2960.2.a.s 3
2960.2.a.t 3
2960.2.a.u 3
2960.2.a.v 4
2960.2.a.w 5
2960.2.a.x 5
2960.2.a.y 5
2960.2.a.z 5
2960.2.a.ba 5
2960.2.a.bb 5
2960.2.a.bc 6
2960.2.d $$\chi_{2960}(2369, \cdot)$$ n/a 108 1
2960.2.e $$\chi_{2960}(369, \cdot)$$ n/a 112 1
2960.2.f $$\chi_{2960}(1481, \cdot)$$ None 0 1
2960.2.g $$\chi_{2960}(2441, \cdot)$$ None 0 1
2960.2.j $$\chi_{2960}(1849, \cdot)$$ None 0 1
2960.2.k $$\chi_{2960}(889, \cdot)$$ None 0 1
2960.2.p $$\chi_{2960}(961, \cdot)$$ 2960.2.p.a 2 1
2960.2.p.b 2
2960.2.p.c 2
2960.2.p.d 2
2960.2.p.e 2
2960.2.p.f 4
2960.2.p.g 6
2960.2.p.h 12
2960.2.p.i 12
2960.2.p.j 12
2960.2.p.k 20
2960.2.q $$\chi_{2960}(1601, \cdot)$$ n/a 152 2
2960.2.r $$\chi_{2960}(1511, \cdot)$$ None 0 2
2960.2.t $$\chi_{2960}(147, \cdot)$$ n/a 904 2
2960.2.v $$\chi_{2960}(1597, \cdot)$$ n/a 904 2
2960.2.y $$\chi_{2960}(1437, \cdot)$$ n/a 904 2
2960.2.ba $$\chi_{2960}(2147, \cdot)$$ n/a 864 2
2960.2.bc $$\chi_{2960}(2399, \cdot)$$ n/a 228 2
2960.2.bd $$\chi_{2960}(179, \cdot)$$ n/a 904 2
2960.2.bg $$\chi_{2960}(221, \cdot)$$ n/a 608 2
2960.2.bh $$\chi_{2960}(741, \cdot)$$ n/a 576 2
2960.2.bk $$\chi_{2960}(339, \cdot)$$ n/a 904 2
2960.2.bm $$\chi_{2960}(1153, \cdot)$$ n/a 224 2
2960.2.bo $$\chi_{2960}(1183, \cdot)$$ n/a 228 2
2960.2.bq $$\chi_{2960}(223, \cdot)$$ n/a 216 2
2960.2.br $$\chi_{2960}(993, \cdot)$$ n/a 224 2
2960.2.bt $$\chi_{2960}(857, \cdot)$$ None 0 2
2960.2.bv $$\chi_{2960}(1703, \cdot)$$ None 0 2
2960.2.bx $$\chi_{2960}(887, \cdot)$$ None 0 2
2960.2.ca $$\chi_{2960}(697, \cdot)$$ None 0 2
2960.2.cc $$\chi_{2960}(931, \cdot)$$ n/a 608 2
2960.2.ce $$\chi_{2960}(149, \cdot)$$ n/a 864 2
2960.2.cf $$\chi_{2960}(1109, \cdot)$$ n/a 904 2
2960.2.ch $$\chi_{2960}(771, \cdot)$$ n/a 608 2
2960.2.ck $$\chi_{2960}(31, \cdot)$$ n/a 152 2
2960.2.cl $$\chi_{2960}(667, \cdot)$$ n/a 864 2
2960.2.cn $$\chi_{2960}(117, \cdot)$$ n/a 904 2
2960.2.cq $$\chi_{2960}(413, \cdot)$$ n/a 904 2
2960.2.cs $$\chi_{2960}(1627, \cdot)$$ n/a 904 2
2960.2.ct $$\chi_{2960}(919, \cdot)$$ None 0 2
2960.2.cx $$\chi_{2960}(1121, \cdot)$$ n/a 152 2
2960.2.cy $$\chi_{2960}(729, \cdot)$$ None 0 2
2960.2.cz $$\chi_{2960}(249, \cdot)$$ None 0 2
2960.2.dc $$\chi_{2960}(841, \cdot)$$ None 0 2
2960.2.dd $$\chi_{2960}(121, \cdot)$$ None 0 2
2960.2.di $$\chi_{2960}(529, \cdot)$$ n/a 224 2
2960.2.dj $$\chi_{2960}(1009, \cdot)$$ n/a 224 2
2960.2.dk $$\chi_{2960}(81, \cdot)$$ n/a 456 6
2960.2.dl $$\chi_{2960}(119, \cdot)$$ None 0 4
2960.2.do $$\chi_{2960}(27, \cdot)$$ n/a 1808 4
2960.2.dq $$\chi_{2960}(917, \cdot)$$ n/a 1808 4
2960.2.dr $$\chi_{2960}(837, \cdot)$$ n/a 1808 4
2960.2.dt $$\chi_{2960}(507, \cdot)$$ n/a 1808 4
2960.2.dw $$\chi_{2960}(911, \cdot)$$ n/a 304 4
2960.2.dx $$\chi_{2960}(51, \cdot)$$ n/a 1216 4
2960.2.dz $$\chi_{2960}(989, \cdot)$$ n/a 1808 4
2960.2.ec $$\chi_{2960}(269, \cdot)$$ n/a 1808 4
2960.2.ee $$\chi_{2960}(251, \cdot)$$ n/a 1216 4
2960.2.eg $$\chi_{2960}(97, \cdot)$$ n/a 448 4
2960.2.eh $$\chi_{2960}(47, \cdot)$$ n/a 456 4
2960.2.ej $$\chi_{2960}(767, \cdot)$$ n/a 456 4
2960.2.el $$\chi_{2960}(177, \cdot)$$ n/a 448 4
2960.2.en $$\chi_{2960}(393, \cdot)$$ None 0 4
2960.2.eq $$\chi_{2960}(1047, \cdot)$$ None 0 4
2960.2.es $$\chi_{2960}(343, \cdot)$$ None 0 4
2960.2.eu $$\chi_{2960}(473, \cdot)$$ None 0 4
2960.2.ew $$\chi_{2960}(939, \cdot)$$ n/a 1808 4
2960.2.ex $$\chi_{2960}(581, \cdot)$$ n/a 1216 4
2960.2.fa $$\chi_{2960}(101, \cdot)$$ n/a 1216 4
2960.2.fb $$\chi_{2960}(859, \cdot)$$ n/a 1808 4
2960.2.fe $$\chi_{2960}(319, \cdot)$$ n/a 456 4
2960.2.fg $$\chi_{2960}(787, \cdot)$$ n/a 1808 4
2960.2.fi $$\chi_{2960}(717, \cdot)$$ n/a 1808 4
2960.2.fj $$\chi_{2960}(637, \cdot)$$ n/a 1808 4
2960.2.fl $$\chi_{2960}(307, \cdot)$$ n/a 1808 4
2960.2.fn $$\chi_{2960}(711, \cdot)$$ None 0 4
2960.2.fr $$\chi_{2960}(289, \cdot)$$ n/a 672 6
2960.2.fs $$\chi_{2960}(321, \cdot)$$ n/a 456 6
2960.2.fu $$\chi_{2960}(49, \cdot)$$ n/a 672 6
2960.2.fw $$\chi_{2960}(169, \cdot)$$ None 0 6
2960.2.fy $$\chi_{2960}(201, \cdot)$$ None 0 6
2960.2.gb $$\chi_{2960}(9, \cdot)$$ None 0 6
2960.2.gd $$\chi_{2960}(41, \cdot)$$ None 0 6
2960.2.ge $$\chi_{2960}(457, \cdot)$$ None 0 12
2960.2.gh $$\chi_{2960}(351, \cdot)$$ n/a 912 12
2960.2.gi $$\chi_{2960}(7, \cdot)$$ None 0 12
2960.2.gl $$\chi_{2960}(247, \cdot)$$ None 0 12
2960.2.gm $$\chi_{2960}(79, \cdot)$$ n/a 1368 12
2960.2.gp $$\chi_{2960}(57, \cdot)$$ None 0 12
2960.2.gq $$\chi_{2960}(13, \cdot)$$ n/a 5424 12
2960.2.gs $$\chi_{2960}(21, \cdot)$$ n/a 3648 12
2960.2.gv $$\chi_{2960}(229, \cdot)$$ n/a 5424 12
2960.2.gx $$\chi_{2960}(133, \cdot)$$ n/a 5424 12
2960.2.gy $$\chi_{2960}(83, \cdot)$$ n/a 5424 12
2960.2.hb $$\chi_{2960}(3, \cdot)$$ n/a 5424 12
2960.2.hd $$\chi_{2960}(531, \cdot)$$ n/a 3648 12
2960.2.hf $$\chi_{2960}(19, \cdot)$$ n/a 5424 12
2960.2.hg $$\chi_{2960}(59, \cdot)$$ n/a 5424 12
2960.2.hi $$\chi_{2960}(91, \cdot)$$ n/a 3648 12
2960.2.hl $$\chi_{2960}(123, \cdot)$$ n/a 5424 12
2960.2.hm $$\chi_{2960}(67, \cdot)$$ n/a 5424 12
2960.2.hp $$\chi_{2960}(573, \cdot)$$ n/a 5424 12
2960.2.hr $$\chi_{2960}(189, \cdot)$$ n/a 5424 12
2960.2.hs $$\chi_{2960}(181, \cdot)$$ n/a 3648 12
2960.2.hu $$\chi_{2960}(533, \cdot)$$ n/a 5424 12
2960.2.hx $$\chi_{2960}(17, \cdot)$$ n/a 1344 12
2960.2.hy $$\chi_{2960}(39, \cdot)$$ None 0 12
2960.2.ia $$\chi_{2960}(287, \cdot)$$ n/a 1368 12
2960.2.id $$\chi_{2960}(127, \cdot)$$ n/a 1368 12
2960.2.if $$\chi_{2960}(311, \cdot)$$ None 0 12
2960.2.ig $$\chi_{2960}(753, \cdot)$$ n/a 1344 12

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2960))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2960)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(148))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(185))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(296))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(370))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(592))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(740))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1480))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2960))$$$$^{\oplus 1}$$